Conventionally, biquad system filter circuits and gyrator system filter circuits are well known as filter circuits suitable to fabricate in IC device. In these filter circuits, their time constants are defined by C/gm, wherein the C and gm are a capacitance of a capacitor and a transconductance of a transconductance circuit, respectively, constituting the filter circuit with each other. The filter characteristic of the filter circuit is optionally defined based on the time constant using a feedback technique. Therefore, in order to obtain a stable filter characteristic it is necessary to keep the time constant C/gm at a constant value.
In general, the capacitance C of capacitors fabricated in IC devices scatter over the order of several percents in relative value, while they further scatter up to several tens of percentages in absolute value. So, in order to keep the time constant C/gm constant, the transconductance gm of the transconductance circuit is required to be adjusted in proportion to the straggling of the capacitance C. In order to construct such a transconductance circuit suitable for IC built-in filters, a so-called gain cell circuit, whose transconductance gm changes in proportion to a bias current applied thereto, or an emitter-coupled differential circuit is conventionally used.
Shown in FIG. 1 is an exemplary gain cell circuit. The gain cell circuit comprises three pairs of transistors, i.e., a first pair of Q1 and Q2, a second pair of Q3 and Q4, and a third pair of Q5 and Q6. The emitters of the transistors Q1 and Q2 whose collectors are coupled to a supply voltage Vcc and also whose bases are coupled to an input signal are coupled to the collectors of the transistors Q3 and Q4 through resistors R1 and R2, respectively. The bases of the transistors Q3 and Q4 are coupled to their own collectors in diode fashion, while their emitters are commonly coupled to a first current source of current I1. Here the first current source will be designated by also I1. Further the collectors of the transistors Q3 and Q4 are coupled to the bases of the transistors Q5 and Q6. The emitters of the transistors Q5 and Q6 are commonly coupled to a second current source of current I2. Here the second current source will be designated by also I2.
Now assuming that the base current amplification factor .beta. of the each transistor is sufficiently large and the resistors R1 and R2 have the same value of resistance R, the transconductance gm of the gain cell circuit shown in FIG. 1 is then represented by Equation (1) in below; EQU gm=I2/[I1.multidot.(R+2.multidot.Re)] (1)
wherein the term Re represents a differentiated emitter resistance.
When the thermal voltage of the each transistor is given by VT, the differentiated emitter resistance Re of the transistors is represented as follows: EQU Re=2.multidot.VT/I1
If R&gt;&gt;Re, the Equation 1 can be approximated as follows; EQU gm=I2I1.multidot.R (2)
Accordingly, the transconductance gm can be adjusted by changing the ratio between the current sources I1 and I2. Normally, the current I1 of the first current source is set in a fixed value while the current I2 of the second current source is set in a variable condition, because of easy setting of bias conditions required in response to the current adjustment.
FIG. 2 shows a typical version of the second current source I2 for supplying an adaptive current. As shown in FIG. 2, the second current source I2 comprises four transistors Q10 through Q13, a variable resistor VR, four resistors R10 through R13, and a power source of supply voltage Vcc. Here the power source will be designated also by the term Vcc. The emitter of the transistor Q10 is connected to the base of the transistor Q11. The base of the transistor Q10 is not only connected to the collector of the transistors Q11, but also connected to the reference potential GND through the resistor R10. The emitter of the transistor Q11 is coupled to the supply voltage Vcc through the resistor R11.
The variable resistor VR is connected across the series circuit of the resistor R11 and the emitter-base junction of the transistor Q11. Further, the collector of the transistor Q10 is connected to a current mirror circuit CM which includes the transistors Q12 and Q13 and the resistors R12 and R13. Thus the current I2 is obtained through the collector of the transistor Q13.
In the circuit shown in FIG. 2, if the resistance of the resistor R10 is assumed to be equal to that of the resistor R11 (R10=R11), the base-to-emitter voltages Vbe of all the transistors Q10 through Q14 are equal to each other, and their base currents Ib are negligibly small, the collector current Ic10 of the transistor Q10 will be represented as follows: EQU Ic10=Vcc/2.multidot.VR (3)
As assumed above that the current output from the current mirror circuit CM is subjected for the current I2 for the second pair of the transistors Q3 and Q4, the following equation is obtained from the above Equations 2 and 3; EQU gm=Vcc/2.multidot.I1.multidot.R.multidot.VR (4)
If the current I1 and the resistance R are constant, the transconductance gm will vary in proportion to the quotient only as follows: EQU gm.perspectiveto.(Vcc/VR) (5)
So if the supply voltage Vcc is stable, there is an advantage that the transconductance gm can be controlled stably at a desired value by the variable resistor VR.
However, in a practical arrangement of the IC built-in filters the respective terms of the Equation 4, i.e., the current I1 of the first current source, the resistance R of the resistors R1 and R2, and the supply voltage Vcc are not constant. Thus, the Equation 5 is hardly realized because of the transconductance gm depends on many variable factors other than the factor of the variable resistor VR.
Further, the differentiated emitter resistance Re is omitted from the Equation 2, but it heavily affects on the transconductance gm in the practical arrangement. These factors fluctuate independently of to the other factors.
In the practical arrangement, therefore, the transconductance gm can not sufficiently controlled by only the current source as shown in FIG. 2. Thus many other circuits have been required in the practical arrangement of such gain cell circuits or the current adjusting circuits.
In the above discussion, such a gain cell circuit has exemplified transconductance circuits. However when an emitter-coupled differential circuit is used, there will occur another problem that a bias current for actuating the circuit must be changed in order to keep the transconductance gm so that the current source as shown in FIG. 2 cannot intrinsically achieve with the stabilization of the transconductance.
The conventional adaptive current generating circuit thus can not sufficiently stabilize the transconductance of the transconductance circuit, so that many complicated stabilizing circuits are required, resulting in an increase in circuit scale. While when the emitter-coupled differential circuit was used as the transconductance circuit, no stabilization of transconductance could be intrinsically achieved.